Home
Class 12
MATHS
If (log)2x+(log)2ygeq6, then the least v...

If `(log)_2x+(log)_2ygeq6,` then the least value of `x+y` is 4 (b) 8 (d) 16 (d) 32

A

4

B

8

C

16

D

32

Text Solution

Verified by Experts

The correct Answer is:
C
Given ` log_(2) x + log_(2) y ge 6`
` rArr log_(2) (xy) ge 6`
` rArr xy ge 64`
Also to define ` log_(2) x and log_(2) y `, we have
` x gt 0, y gt 0`.
Since A.M.` ge G.M., `we have
` (x+y)/2 ge sqrt(xy)`
` or x + y ge 2 sqrt(xy) ge 16`
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise (Multiple)|17 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise (Comprehension)|6 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise 1.6|6 Videos

  • LOGARITHM AND ITS APPLICATIONS

    CENGAGE|Exercise Subjective Type|9 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

Similar Questions

Explore conceptually related problems

if (log)_y x+(log)_x y=2,x^2+y=12 , the value of x y is 9 (b) 12 (c) 15 (d) 30

If log_2x+log_(4)x+log_(16)x=7/2 , find the value of x.

If (log)_3{5+4(log)_3(x-1)}=2, then x is equal to 4 (b) 3 (c) 8 (d) (log)_2 16

If x y^2=4a n d(log)_3((log)_2x)+(log)_(1/3)((log)_(1/2)y)=1 ,then x equals (a) 4 (b) 8 (c) 16 (d) 64

If log ((x+y)/3)=1/2 (log x +log y) then find the value of x/y+y/x

The greatest integral value of a such that sqrt( 9 - a^2 + 2x - x^2) >= sqrt(16 - x^2) for at least one positive value of x is (a) 3 (b) 4 (c) 6 (d) 7

Log f(x)=log((log)_(1//3)((log)_7(sinx+a))) be defined for every real value of x , then the possible value of a is 3 (b) 4 (c) 5 (d) 6

If (a+(log)_4 3)/(a+(log)_2 3)=(a+(log)_8 3)/(a+(log)_4 3)=b ,then b is equal to 1/2 (2) 2/3 (c) 1/3 (d) 3/2

If (log)_2x+(log)_x2=(10)/3=(log)_2y+(log)_y2a n dx=y ,t h ex+y= 2 (b) 65/8 (c) 37/6 (d) none of these

CENGAGE-LOGARITHM AND ITS PROPERTIES-Exercise (Single)
  1. If the equation 2^x+4^y=2^y is solved for y in terms of x where x<0, t...

    Text Solution

    |

  2. The number of solution of x^(log)x(x+3)^2=16 is a)0 (b) 1 (c) 2 (d...

    Text Solution

    |

  3. The product of roots of the equation (log8(8/x^2))/((log8x)^2)=3 is 1 ...

    Text Solution

    |

  4. Let a >1 be a real number. Then the number of roots equation a^(2(log)...

    Text Solution

    |

  5. The number of roots of the equation (log)(3sqrt("x"))x+(log)(3x)sqrt(x...

    Text Solution

    |

  6. The set of all x satisfying the equation x^(log)3x^2+((log)3x)^(2-10)=...

    Text Solution

    |

  7. Number of real values of x satisfying the equation (log)2(x^2-x)(log)...

    Text Solution

    |

  8. Find the value of x satisfying the equations log(3)(log(2)x)+log(1//3)...

    Text Solution

    |

  9. If x1a n dx2 are the roots of the equation e^2 x^(lnx)=x^3 with x1> x2...

    Text Solution

    |

  10. The number of real values of the parameter k for which (log(16)x)^2-(l...

    Text Solution

    |

  11. x^((log)5x)>5 implies x in (0,oo) (b) [2,2.5] (c) (2,2.5) (d) (0,2...

    Text Solution

    |

  12. If S={x in N :2+(log)2sqrt(x+1)>1-(log)(1/2)sqrt(4-x^2)} , then S={1...

    Text Solution

    |

  13. If S={x in R :((log)(0. 6)0. 216)(log)5(5-2x)lt=0}, then S is equal t...

    Text Solution

    |

  14. Solution set of the inequality 1/(2^x-1)>1/(1-2^(x-1)) is 1,oo) (b) 0...

    Text Solution

    |

  15. If (log)2x+(log)2ygeq6, then the least value of x+y is 4 (b) 8 (d...

    Text Solution

    |

  16. Which of the following is not the solution log(x)(5/2-1/x) gt (5/2-1/x...

    Text Solution

    |

  17. The solution set of the inequality (log)(10)(x^2-16)lt=(log)(10)(4x-11...

    Text Solution

    |

  18. Solution set of the inequality (log)(0. 8)((log)6(x^2+x)/(x+4))<0 is )

    Text Solution

    |

  19. Which of the following is not the solution of (log)3(x^2-2)<(log)3(3/2...

    Text Solution

    |

  20. The true solution set of inequality (log)((x+1))(x^2-4)>1 is equal to ...

    Text Solution

    |